Calculus of Variations and Partial Differential Equations

期刊简介：Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives.This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include:- Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory- Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems- Variational problems in differential and complex geometry- Variational methods in global analysis and topology- Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems- Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions- Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.

【译文】变分法和偏微分方程是经典、非常活跃且密切相关数学领域，在微分几何和数学物理中有重要应用。在过去四十年中，这一主题在全球范围内得到了蓬勃发展，并且仍在继续扩展和拓展到更广泛的视角。这本期刊将吸引并收集该研究领域的重要高质量贡献，并强调分析家、几何学家和物理学家之间的相互作用。变分法和偏微分方程领域广泛；然而，该期刊将开放于所有有趣的新发展。涵盖的主题包括：- 变分积分的最小化问题，最小值和临界点的存在性和正则性理论，几何测度理论- 偏微分方程的变分方法，最优质量运输，线性和非线性特征值问题- 微分和复几何中的变分问题- 全局分析和拓扑中的变分方法- 动态系统、辛几何、哈密顿系统周期解- 数学物理中的变分方法，非线性弹性，渐近变分问题，均匀化，毛细现象，自由边界问题和相变- Monge-Ampère 方程以及其他与微分几何、复几何和物理问题相关的完全非线性偏微分方程。